Cramer's Rule — Quiz

Question 1 • Advanced Algebra: Concepts and Connections

Which equation can be used to determine x -value of the solution in the given system of linear equations? negative 2 x plus 14 y is equal to 148 3 x plus 5 y is equal to 246

Answer

the fraction with numerator the 2 by 2 matrix, row 1, column 1, negative 2 column 2, 148 row 2, column 1, 3 column 2, 246 and denominator the 2 by 2 matrix, row 1, column 1, negative 2 column 2, 14 row 2, column 1, 3 column 2, 5 is equal to 52

the fraction with numerator the 2 by 2 matrix row 1, 148 14 row 2, 246 5 and denominator the 2 by 2 matrix, row 1, column 1, negative 2 column 2, 14 row 2, column 1, 3 column 2, 5 is equal to 52

the fraction with numerator the 2 by 2 matrix row 1, 148 14 row 2, 246 5 and denominator the 2 by 2 matrix, row 1, column 1, negative 2 column 2, 14 row 2, column 1, 3 column 2, 5 is equal to 18

Explanation

By Cramer’s rule, the x-value is found by replacing the x-coefficient column with the constants, then dividing by the determinant of the coefficient matrix. This gives det([[148, 14], [246, 5]]) / det([[-2, 14], [3, 5]]) = (148·5 − 14·246) / ((−2)·5 − 14·3) = (−2704)/(−52) = 52. This is choice D.

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